Recent detections of gamma-ray burst (GRB) counterparts confirm their great distances and consequent potential use as cosmic probes. However, GRB diversity may thwart this idea. The scatter of intrinsic GRB properties could easily mask the extrinsic effect of cosmological time dilation. Current investigations examine the question of temporal self-similarity: Extrinsic time dilation must be manifest with the same factor on all GRB timescales as a function of distance. Here we show that time-reversal-independent analysis of GRB time profiles using a peak alignment methodology reveals average profiles with approximately equal rise and decay timescales, per peak-flux group, except for the dimmest group. This departure from self-similarity is consistent with a selection effect: At sufficiently low peak fluxes, the BATSE causal trigger misses dim, slowly rising bursts. Interestingly, for GRB970508, the redshift-corrected time-dilation factor inferred for its peak flux is consistent with the measured redshift,z=0.835,if bright bursts lie at redshifts of a few tenths. ©1998 American Institute of Physics.